Rolling contact between a rubber ring and rigid cylinders: Mechanics of rubber belts

We revisit the classical creep theory for a belt drive system as a rolling contact problem between a rubber ring and rigid cylinders to evaluate the effects of linear viscoelasticity and large strain of the belt on the system in a steady state. We first construct the general theory of belt mechanics for a multi-pulley system by dimensional reduction from 3D extensible, unshearable rod. We then develop the belt mechanics for a linear viscoelastic belt and show that the effect of retardation time can be involved in the effective friction coefficient: the classical Euler's belt formula can be recovered. Next, we assume that the belt is a neo-Hookean material and examine the effect of large strain of the belt on the contact pressure distribution. We compare the theory with the results by finite element analysis and show that the theory provides good quality.

► The classical creep theory for a rubber belt drive system is revisited.
► The effect of linear viscoelasticity of the belt is appeared as the effective friction coefficient.
► The nonlinear elastic belt gives a higher contact pressure than the linear elastic belt.
► The present theory can reasonably predict the contact pressure distribution at large strain.